Stress-difference index for graphs

The stress of a vertex is a node centrality index, which has been introduced by Shimbel (1953). The stress of a vertex in a graph is the number of geodesics (shortest paths) passing through it. A topological index of a chemical structure (graph) is a number that correlates the chemical structure with chemical reactivity or physical properties. In this paper, we introduce a new topological index for graphs called stress-difference index using stresses of vertices. Further, we establish some inequalities, prove some results and compute stress-difference index for some standard graphs. Also, we found that there is a positive correlation between the stress-difference index and some physical properties of lower alkanes.